Jay Rodriguez's solo goal rescued a point for Burnley and denied Peterborough their first Championship win since Boxing Day.
The 22-year-old striker slotted home three minutes from the end after a mazy run past four Posh defenders.
Paul Taylor had put the visitors ahead after a mistake from Ben Mee, before David Ball came close to a second.
Chris McCann headed over for the Clarets, who also had a penalty appeal turned down, before Rodriguez's strike.
The draw leaves Burnley just two points, but five places, off the play-off places while Peterborough have taken only two points taken from five league games in 2012.
Taylor smashed past goalkeeper Lee Grant after Mee's slip had let him in and Peterborough were within a post's width of doubling their lead when Ball's shot rebounded off the woodwork.
Charlie Austin drew a great save from Joe Lewis at the other end in a rare first-half chance for the hosts before seeing an effort cleared off the line from a Josh McQuoid cross after the break.
Referee Colin Webster waved away the home side's appeals for a penalty when Ross Wallace's shot hit defender Mark Little, but Rodriguez had the last say with a special goal.
Burnley 01 Grant 02 Trippier 04 Duff 15 Edgar 36 Mee (Bartley - 76' ) 06 McCann 07 Wallace 08 Marney (Hines - 83' ) 19 McQuoid (Treacy - 70' ) 09 Rodriguez 23 Austin Substitutes 12 Jensen 24 Easton 20 Bartley 26 Treacy 16 Hines Peterborough United 01 Lewis 02 Little 04 Bennett 05 Zakuani 27 Alcock 11 McCann 14 Rowe 23 Frecklington (Tunnicliffe - 70' ) 09 Ball (Tomlin - 75' ) 10 Boyd 26 Taylor Substitutes 28 Jones 16 Tunnicliffe 21 Kearns 08 Tomlin 12 Sinclair